The most common and most likely answer to this crossword clue is the 9 letter word QUODLIBET
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Buddy explains!
The straight part
We know that "Argument" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case argument = quodlibet.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.
What does QUODLIBET mean?
QUODLIBET noun- A form of music with melodies in counterpoint.
- A form of trompe l'oeil which realistically renders domestic items (paper-knives, playing-cards, ribbons, etc).
- A mode of philosophical debate popular in the Middle Ages, in which any question could be posed extemporaneously.